Many electrical devices have two modes of operation: an active mode in which a load is connected to the output, and a standby mode in which no load (actually a very small load) is connected at the output. In active mode, the power supplied should be sufficient for the device to perform its usual functions and, in standby mode, minimal power should be expended: in most cases, just enough for the device to be switched back into active mode when necessary.
It is becoming increasingly important to conserve energy and reduce power losses and power supplies which have minimal power consumption during standby mode are becoming more and more desired. Such power supplies find applications in many situations, for example as standby power supplies in electrical devices (e.g. in televisions, washing machines) or within external power supplies for supplying power to detect whether an electrical device is connected or not and to switch on the main power supply (e.g. within a portable telephone charger where the telephone is placed in a cradle for charging).
Note that, throughout this specification, the terms “no-load mode” and “standby mode” are used interchangeably. Although, strictly speaking, the output load during standby is not zero, the load is extremely small and can be approximated to zero for all practical purposes.
FIG. 1 shows one conventional arrangement of a transformer used in a power supply for a device which has a standby mode, for stepping down the voltage from the AC supply. The transformer 101 comprises a primary winding 101a and secondary windings 101b, 101c and 101d. The primary winding 101a is connected to an AC supply 103 via a switch 105. When switch 105 is closed, power is supplied to the transformer 101. Secondary winding 101b provides the supply voltage to standby circuit 107 and secondary windings 101c and 101d provide the supply voltage to the main device 109 (i.e. the output load) via switches 111 and 113 respectively. The main device 109 may be put into standby mode by opening switches 111 and 113 so that the supply voltage is no longer supplied to the main device 109. Those switches 111 and 113 may be operated by standby circuit 107 directly, by remote control or under some other form of control (e.g. automatic standby after a given period of time).
The design of a transformer such as transformer 101 in FIG. 1 is based on the power requirement of the device when in active mode. This may vary if the device is arranged to perform a number of different tasks each requiring a different power input. Once the maximum power requirement of the device during active mode has been determined, the transformer is then designed to deliver that maximum power (for at least some of the time) most economically (e.g. using the smallest possible amount of material) and with the smallest rise in temperature.
Referring once again to FIG. 1, when the device is put into standby mode by a user, standby circuit 107 cuts off the power supply to the main device 109 by opening switches 111 and 113. During standby mode, standby circuit only requires a small amount of power: in most cases, just enough to be able to switch the device back into active mode. Hence, during standby mode, the transformer 101 is actually much larger than required which means that its operation is rather inefficient. In that case, most of the power loss is due to the no-load losses from the primary winding of the transformer itself. These no-load losses consist mainly of core losses, which include hysteresis losses and eddy-current losses in the magnetic core, and copper losses due to the current flowing through the copper wire of the winding, which has a finite resistance. These three types of losses will be discussed further below.
FIG. 2 shows an inductor coil having N turns, on a magnetic coil with an applied voltage. This is a close approximation to the primary winding of a transformer (such as transformer 101 in FIG. 1) when in no-load mode.
According to Faraday's law, the voltage is proportional to the rate of change of the magnetic flux:
                    v        =                  N          ⁢                                    ⅆ              ϕ                                      ⅆ              t                                                          (        1        )            where v is the applied voltage, N is the number of turns in the primary winding and φ is the total magnetic flux through the winding.
If we assume a sinusoidal input voltage having frequency ω i.e. one of the form ν=√{square root over (2)}V cos ωt, substituting this into equation (1) gives us:
                                          N            ⁢                                          ⅆ                ϕ                                            ⅆ                t                                              =                                    2                        ⁢            V            ⁢                                                  ⁢            cos            ⁢                                                  ⁢            ω            ⁢                                                  ⁢            t                          ⁢                                  ⁢                  ϕ          =                                                    1                N                            ⁢                              ∫                                                      2                                    ⁢                  V                  ⁢                                                                          ⁢                  cos                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                                      =                                                                                2                                    ⁢                  V                                                  N                  ⁢                                                                          ⁢                  ω                                            ⁢              sin              ⁢                                                          ⁢              ω              ⁢                                                          ⁢              t                                                          (        2        )            
If we assume a uniform flux distribution, the magnetic flux density B is given by:
                    B        =                  ϕ          A                                    (        3        )            where A is the cross sectional area of the core.
Substituting equation (3) into equation (2) gives us:
  AB  =                              2                ⁢        V                    N        ⁢                                  ⁢        ω              ⁢    sin    ⁢                  ⁢    ω    ⁢                  ⁢    t  
The maximum flux density Bmax is given when sin ωt=1. This gives:
                              B          max                =                                            2                        ⁢            V                                AN            ⁢                                                  ⁢            ω                                              (        4        )            
The three types of losses, discussed above (hysteresis losses, eddy-current losses and copper losses) are given by equations (5), (6) and (7) below.
The hysteresis loss Ph is given by:Ph=Khf(Bmax)α  (5)where f is the excitation frequency, α is the Steinmetz exponent which will depend on the particular properties of the material used for the core (usually taken to be between 1.6 and 2.0) and Kh is another constant also dependent on the particular properties of the core material.
The eddy current loss Pe is given by:Pe=Kef2(Bmax)2  (6)where f is the excitation frequency and Ke is a constant dependent on the particular properties of the core material.
The copper loss PCu is given by:PCu=IRMS2R  (7)where IRMS is the root-mean-squared current through the winding and R is the effective impedance of the winding.
From equation (5), we see that, for the hysteresis loss:
            P      h        ∝                  (                  B          max                )            α        and            P      h        ∝          1              N        α            
From equation (6), we see that for the eddy-current loss:
            P      e        ∝                  (                  B          max                )            2        and            P      e        ∝          1              N        2            
That is, the core losses Ph and Pe increase as Bmax is increased but decrease as the number of turns N is increased.
The reader may assume from the above that the transformer should necessarily be designed with as many turns as possible in the windings in order to decrease Bmax as far as possible and hence reduce the core losses. However, this is not the case because the design of a transformer is based on the power requirement of the device when in active mode and the aim of the transformer is to deliver the required power most economically.